Conventionally, an air-fuel ratio control apparatus has been widely known, which comprises a three-way catalytic converter disposed in an exhaust gas passage of an internal combustion engine, and an upstream air-fuel ratio sensor and a downstream air-fuel ratio sensor, disposed upstream and downstream of the three-way catalytic converter, respectively. The air-fuel ratio control apparatus calculates an air-fuel ratio feedback amount based on an output of the upstream air-fuel ratio sensor and an output of the downstream air-fuel ratio sensor, and performs a feedback control on an air-fuel ratio of a mixture supplied to the engine (an air-fuel ratio of the engine) with the air-fuel ratio feedback amount, so that the air-fuel ratio of the engine coincides with the stoichiometric air-fuel ratio. Further, an air-fuel ratio control apparatus has also been proposed, which calculates an air-fuel ratio feedback amount based solely on either the output of the upstream air-fuel ratio sensor or the output of the downstream air-fuel ratio sensor, and performs a feedback control on the air-fuel ratio of the engine with the air-fuel ratio feedback amount. The air-fuel ratio feedback amount used in those air-fuel ratio control apparatuses is a control amount commonly used for all of the cylinders.
Meanwhile, an electronic control fuel injection type internal combustion engine, typically, comprises at least one fuel injector in each of the cylinders or in each of the intake ports, each communicating with each of the cylinders. Accordingly, when a characteristic (or property) of the injector for a specific cylinder becomes a “characteristic that the injector injects a fuel by (or of) an amount larger (more excessive) than an instructed fuel injection amount”, only an air-fuel ratio of a mixture supplied to the specific cylinder (air-fuel-ratio-of-the-specific-cylinder) changes toward extremely richer side. That is, a non-uniformity among air-fuel ratios of the cylinders (a variation in air-fuel ratios among the cylinders, an air-fuel ratio imbalance among the cylinders) becomes large. In other words, there arises an imbalance (a non-uniformity) among the individual-cylinder-air-fuel-ratios.
In this case, an average of the air-fuel ratios of the mixtures supplied to the entire engine becomes an air-fuel ratio richer (smaller) than a stoichiometric air-fuel ratio. Accordingly, the air-fuel ratio feedback amount common to all of the cylinders causes the air-fuel ratio of the specific cylinder to change to a leaner (larger) air-fuel ratio so that the air-fuel ratio of the specific cylinder is made closer to the stoichiometric air-fuel ratio, and at the same time, the air-fuel ratio feedback amount causes each of the air-fuel ratios of the other cylinders to change to a leaner (larger) air-fuel ratios so that each of the air-fuel ratios of the other cylinders is made deviate more from the stoichiometric air-fuel ratio. As a result, the average of the air-fuel ratios of the mixtures supplied to the entire engine is made roughly equal to the stoichiometric air-fuel ratio.
However, the air-fuel ratio of the specific cylinder is still richer (smaller) than the stoichiometric air-fuel ratio, and the air-fuel ratios of the other cylinders are leaner (larger) than the stoichiometric air-fuel ratio, and therefore, a combustion condition of the mixture in each of the cylinders is different from a perfect combustion. As a result, an amount of emissions (an amount of an unburnt substances and an amount of nitrogen oxides) discharged from each of the cylinders increases. Accordingly, although the average of the air-fuel ratios of the mixtures supplied to the engine coincides with the stoichiometric air-fuel ratio, the three-way catalytic converter can not purify the increased emission, and thus, there is a possibility that the emission becomes worse. It is therefore important to detect whether or not the air-fuel ratio non-uniformity among cylinders is excessively large (the air-fuel ratio imbalance among cylinders state is occurring) so that an appropriate measure can be taken, in order not to worsen the emissions. It should be noted that the air-fuel ratio imbalance among cylinders occurs due to various reasons, such as when a characteristic of an injector of a specific cylinder becomes a “characteristic that the injector injects the fuel by (or of) an amount which is excessively smaller than the instructed fuel injection amount”, or when distribution ratio of an EGR gas and an evaporated fuel gas to each of the cylinders becomes non-uniform.
One of such conventional apparatuses that determine whether or not the air-fuel ratio imbalance among cylinders state is occurring obtains a trajectory length of an output (output signal) of an air-fuel ratio sensor (the above mentioned upstream air-fuel ratio sensor) disposed at an exhaust-gas-aggregated-portion onto which exhaust gases from a plurality of cylinders merge, compares the trajectory length with an “reference value varying in accordance with an engine rotational speed and an intake air amount”, and the determines whether or not the air-fuel ratio imbalance among cylinders state is occurring based on the comparison result (refer to, for example, U.S. Pat. No. 7,152,594). It should be noted that, in the present specification, determining (judging) whether or not the air-fuel ratio imbalance among cylinders state is occurring can be simply referred to as a “determination of an air-fuel ratio imbalance among cylinders, or an imbalance determination”.